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Topic: Decidable

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	Ian Hodkinson: monodic fragments of first-order temporal logic
		This paper proves decidability of satisfiability of sentences of the monodic packed fragment of first-order temporal logic with equality and connectives Until and Since, in models with various flows of time and domains of arbitrary cardinality.
		The aim of this paper is to summarize and analyze some results obtained in 2000--2001 about decidable and undecidable fragments of various first-order temporal logics, give some applications in the field of knowledge representation and reasoning, and attract the attention of the `temporal community' to a number of interesting open problems.
		Decidable and undecidable fragments of first-order branching temporal logics
	www.doc.ic.ac.uk /~imh/frames_website/monodic.html (908 words)

	Citations: A decidable class of bounded recursions - Naughton, Sagiv (ResearchIndex)
		Another corollary of the two theorems is that stability of a query with conjuncts and disjuncts is also decidable, since such a query can be translated into an equivalent UCQ.
		A decidability undecidability border, for cases of different syntactical restrictions and semantical assumptions has been studied in many papers, including [S85] CK86] A89] CGKV88] GMSV93] HKMV91] V88] and [W95] The syntactical restrictions considered were: number of recursive rules....
		The decidability undecidability border, for cases of different syntactical restrictions and semantical assumptions has been studied in [20] 5] 2] 6] 8] 9] 24] 23] The syntactical restrictions considered were: number of rules or of recursive rules in the program, maximal arity of....
	citeseer.ist.psu.edu /context/62059/0 (980 words)

	decidability from FOLDOC (Site not responding. Last check: )
		Decidability is an important concept in computability theory.
		"all numbers with a 5 in them") is said to be "decidable" if I can write a program (usually for a Turing Machine) to determine whether a number is in the set and the program will always terminate with an answer YES or NO after a finite number of steps.
		Most sets you can describe easily are decidable, but there are infinitely many sets so most sets are undecidable, assuming any finite limit on the size (number of instructions or number of states) of our programs.
	foldoc.org /?decidable (297 words)

	The result on the previous page can also be stated as : A set S is decidable iff both S and ~S are r
		Theorem: A set S is decidable iff both S and ~S are Turing languages.
		The result on the previous page can also be stated as : A set S is decidable iff both S and ~S are r.e.
		Corollay: Every infinitie decidable set can be split into 2 disjoint infinitie decidable subsets.
	www.runet.edu /~jhelm/classes/420/decidable2.htm (1326 words)

	decidability from FOLDOC (Site not responding. Last check: )
		Decidability is an important concept in computability theory.
		"all numbers with a 5 in them") is said to be "decidable" if I can write a program (usually for a Turing Machine) to determine whether a number is in the set and the program will always terminate with an answer YES or NO after a finite number of steps.
		Most sets you can describe easily are decidable, but there are infinitely many sets so most sets are undecidable, assuming any finite limit on the size (number of instructions or number of states) of our programs.
	www.foldoc.org /?decidable (297 words)

	Decidable Logical Theories
		Students should become familiar with the principal decidability results in the area of logical theories and with the basic methods involved, especially quantifier elimination.
		Chapter 3 deals with the theories of algebraically closed and real closed fields; the latter is one of the most famous examples of a decidable logical theory, and many algorithm have been developed in the past.
		Chapter 4 shows how the decidability of the theory of some class of algebraic structures carries over to cartesian products and generalized products of such structures; this is used to show the decidability of the theory of abelian groups.
	www.risc.uni-linz.ac.at /education/courses/ws2004/dlt (294 words)

	partially decidable problem
		Equivalently, there exists an algorithm that halts and outputs 1 for every instance having a "yes" answer, but for instances having a "no" answer is allowed either not to halt or to halt and output 0.
		See also decidable problem, undecidable problem, solvable, tractable, computable.
		Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "partially decidable problem", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/partiallyDecidableProb.html (154 words)

	Citations: Decidable Optimization Problems for Database Logic Programs - Cosmadakis, Gaifman, Kanellakis, Vardi ...
		In the present paper we propose a proof that the eliminability of recursion from arbitrarily nested L formulae does indeed constitute a decidable problem.
		In view of this negative result, researchers attempted to find large classes of Datalog programs for which boundedness is decidable, and also to identify the sources of undecidability.
		Predicate Boundedness of Linear Monadic Datalog is in PSPACE - van der Meyden (1990)
	citeseer.ist.psu.edu /context/153846/0 (3163 words)

	S.O.S. Mathematics CyberBoard :: View topic - Turing-recognizable/Decidable
		As I know if a language is decidable aka rec, then that means there exists a TM that will halt on the input and output either an accept or a reject.
		I say yes because for a language to be recognizable it has to be in the intersection of rec and co-re.
		If a language L is decidable, then there exists a Turing machine for the language which halts on every input.
	www.sosmath.com /CBB/viewtopic.php?t=16142 (380 words)

	decidable language
		Definition: A language for which membership can be decided by an algorithm that halts on all inputs in a finite number of steps --- equivalently, can be recognized by a Turing machine that halts for all inputs.
		Note: For emphasis, the equivalent term totally decidable language is sometimes used.
		Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "decidable language", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/decidableLanguage.html (163 words)

	Coq.Logic.Decidable
		not_and : (A,B:Prop) (decidable A) -> ~(A/\B) -> ~A \/ ~B. Unfold decidable; Tauto.
		not_imp : (A,B:Prop) (decidable A) -> ~(A -> B) -> A /\ ~B. Unfold decidable;Tauto.
		imp_simp : (A,B:Prop) (decidable A) -> (A -> B) -> ~A \/ B. Unfold decidable; Tauto.
	pauillac.inria.fr /cdrom/www/coq/library/Coq.Logic.Decidable.html (103 words)

	Analysis and Mechanisation of Decidable First-Order Temporal Logics
		This is a 30 month EPSRC funded project which started in November 2001 in London and in March 2002 in Liverpool.
		The London part of the project ended 31st March 2004 and the Liverpool part ended on 3rd April 2005.
		In this project we will investigate FOTL in depth, and develop, implement, and analyse tools mechanising the axiomatisable and decidable fragments of FOTL identified.
	www.csc.liv.ac.uk /~clare/projects/fotl/fotl.html (99 words)

	Bisimulation Equivalence is Decidable for all Context-Free Processes
		Abstract: For finite-state processes all known behavioural equivalences can be seen to be decidable.
		In 1987, Baeten, Bergstra and Klop showed the surprising result that bisimulation equivalence is decidable for a subclass of such processes, the so-called normed processes where termination is always possible.
		In this paper we generalize this result by showing that bisimulation is decidable for all context-free processes using a technique inspired by Caucal's proof of the decidability of language equivalence for simple algebraic grammar.
	www.lfcs.inf.ed.ac.uk /reports/92/ECS-LFCS-92-218/index.html (145 words)

	decidable - OneLook Dictionary Search
		Decidable : Eric Weisstein's World of Mathematics [home, info]
		Example: "The vote in New Hampshire often decides the outcome of the Presidential election"
		Phrases that include decidable: decidable problem, totally decidable problem
	www.onelook.com /?w=decidable (167 words)

	Deciding When And How To Effectively Use A Legal Administrator
		he basic factors for the 1-10 lawyer firm to consider in deciding to hire a full-time administrator are:
		Each firm will decide the timing for adding this key member to it's management team.
		However, the question of whether or not to add a business manager is moot - the only question is "why has the firm waited so long to make this decision and how does the firm locate and hire a mutually compatible person to fill this key position?"
	rd.business.com /index.asp?epm=s.1&bdcq=Decidable&bdcr=3&bdcu=http://weilandco.com/new/article.html&bdcp=&partner=2662601&bdcs=nwuuid-2662601-08C484EF-F53E-7210-4BB9-1531CAA57EF5-ym (1273 words)

	Decidable Summary
		Decidable and Undecidable Theories Suppose T is a theory (i.e., a set of sentences) in a formal language L of logic.
		A decision procedure for T is a mechanical procedure for calculating whether any given sentence of L is a logical consequence of T.
		The word decidable has formal meaning in computability theory, the theory of formal languages, and mathematical logic.
	www.bookrags.com /Decidable (113 words)

	CSE237 Lecture 22, Spring 2006
		We've used reductions before to decide one language by using decider for another one.
		Now we are using the other direction: to show that a new language is not decidable because another one is not.
		is not decidable; this is our first example of a language that's recognizable but not decidable.
	www.cse.uconn.edu /~dqg/cse237/L22.html (348 words)

	Herbrand Logic -- First-order Syntax and Herbrand Semantics
		That problem is not semi-decidable (otherwise solving the Diophantine itself would be decidable), ensuring that Herbrand Entailment is not semi-decidable.
		Proof: Because entailment and therefore unsatisfiability in the fragment with ∀* premises and ∃* queries is semi-decidable, satisfiability of that fragment must not be semi-decidable.
		This statement in this Corollary was made earlier with the condition that checking whether a candidate proof actually proves a conjecture is decidable.
	logic.stanford.edu /~thinrich/herbrand/html/modeltheory-prooftheory.html (1976 words)

	Behavioural Equivalence for Infinite Systems - Partially Decidable! (Site not responding. Last check: )
		More interestingly, we show that they are decidable, contrasting a result of Hirshfeld that standard interleaving language equivalence is undecidable.
		We show that for a certain non-trivial subclass of processes between BPP and TCSP, not only are the two equivalences different, but one (locality) is decidable whereas the other (pomsets) is not.
		The decidability result for locality is proved by a reduction to the reachability problem for Petri nets.
	www.brics.dk /RS/95/55 (223 words)

	PHIL 2340: Decidability
		A yes-or-no question is decidable if there is a procedure that is guaranteed to give an answer to the question in a finite amount of time.
		A logical system such as a system of propositional logic or a system of first-order logic is decidable if, for every argument expressible in the language of the system, the question whether the argument is valid is decidable.
		Rather, the issue of decidability concerns the more precise and restricted conceptions of validity developed for propositional logic and first-order logic.
	www.trinity.edu /cbrown/logic/decidability.html (1313 words)

	[No title]
		Then supposing "script-H were decidable" allows us to conclude that the moon is made of green cheese, because a FALSE HYPOTHESIS logically implies any assertion at all, and we know that the hypothesis that script-H is decidable is indeed false.
		QED We think of Scheme^{script-A} as Scheme extended with the ability to decide script-A. So any set script-B which is decidable -- that is, decidable in "real", unextended Scheme -- will certainly be decidable when Scheme is extended.
		is its decider -- and hence by THEOREM 2 is script-A half-decidable.
	theory.lcs.mit.edu /classes/6.044/fall96/handouts/H26-relative-computability (1207 words)

	Re: Decidable polymorphic recursion? (Site not responding. Last check: )
		What I am looking for is a type system for which we can > infer the types but still gives some kind of (but of course not > full) polymorphic recursion.
		A paper on decidable type inference for polymorphic recursion is available at http://www.linc.dcc.ufmg.br/~lucilia/research/ml0-toplas.ps.gz.
		The abstract follows: ==================================================================== This article presents a type system for polymorphic recursion that has decidable type inference.
	www.seas.upenn.edu /~sweirich/types/archive/1999-2003/msg00915.html (197 words)

	Amazon.com: decidable (Site not responding. Last check: )
		Decidable Theories II (Lecture Notes in Mathematics, 328) by J. Richard Buchi and Dirk Siefkes (Paperback - 1973)
		Lambda definability is decidable for second order types and for regular third order types (Technical report / University at Buffalo, State University of New York, Dept. of Computer Science) by Marek Zaionc (Unknown Binding - 1995)
		Decidable subcases of the equivalence problem for recursive program schemes (Technical report.
	www.amazon.com /s?ie=UTF8&keywords=decidable&tag=lexico&index=blended&link_code=qs&page=1 (486 words)

	A Decidable Temporal Logic of Parallelism, Mark Reynolds
		In this paper we shall introduce a simple temporal logic suitable for reasoning about the temporal aspects of parallel universes, parallel processes, distributed systems, or multiple agents.
		We will use a variant of the mosaic method to prove decidability of this logic.
		This shows that the mosaic method is sometimes a stronger way of establishing decidability.
	projecteuclid.org /getRecord?id=euclid.ndjfl/1039700748 (582 words)

	RR-1837 : Decidable properties and optimal normalization in persistent term rewriting systems
		We establish criteria for weak and strong normalization of terms in PTRSs and prove that they are decidable.
		Nous presentons d'autres resultats de decidabilite dans les systemes persistents, l'equivalence syntaxique de deux systemes est decidable (et nous en donnons un critere simple) ainsi que le probleme de la reductibilite.
		En outre, pour tout terme t normalisable, nous prouvons que le nombre d'etapes de la reduction optimale qui calcule le forme normale de t est egal au nombre minimal de familles de radicaux contracte par une reduction normalisante issue du terme t.
	www.inria.fr /rrrt/rr-1837.html (393 words)

	FOM: Decidable?
		So take \phi(2) to be the sentence that you want to decide in the expanded language and, treating 2 as a variable, decide \forall 2 ((2 is prime) -> \phi(2)) using the original decision procedure.
		Alternately, you could use automata on finite trees in much the same way that automata on finite strings can be used to decide Presburger arithmetic.
		An integer can be encoded as the sequence of it's (binary encoded) prime exponents coming off of a main trunk.
	www.cs.nyu.edu /pipermail/fom/2002-April/005433.html (230 words)

	Deciding On The Advertising Media
		Advertising agencies are usually quite good at producing creative radio commercials.
		The task of deciding what your mailing should have as content, its design and its message(s) is up to you.
		Second, decide what you are going to say on the item.
	rd.business.com /index.asp?epm=s.1&bdcq=Decidable&bdcr=1&bdcu=http://www.bizmove.com/marketing/m2j4.htm&bdcp=&partner=2662601&bdcs=nwuuid-2662601-08C484EF-F53E-7210-4BB9-1531CAA57EF5-ym (5519 words)

	[No title]
		First of all, what do we mean by a "major purchase?" Among financial types (like your banker or accountant), the main consideration is usually that the item or project will have a service period of more than a year.
		If so, you'd want to spend at least some time studying the issue, and doing what is known as "capital budgeting." If the item will last for less than a year, it's probably not worth a detailed analysis — you might decide to just "get it if you need it."
		Some business owners also like to draw the line at a certain dollar amount — depending on the size of your operation, this can be $1,000, $10,000, or any other amount that makes sense.
	rd.business.com /index.asp?epm=s.1&bdcq=Decidable&bdcr=2&bdcu=http://www.toolkit.cch.com/text/p06_6100.asp&bdcp=&partner=2662601&bdcs=nwuuid-2662601-08C484EF-F53E-7210-4BB9-1531CAA57EF5-ym (639 words)

	Henzinger/Kopke/Puri/Varaiya: What's Decidable about Hybrid Automata?
		Many verification tasks for such programs can be expressed as reachability problems for hybrid automata.
		By improving on previous decidability and undecidability results, we identify the precise boundary between decidability and undecidability of the reachability problem for hybrid automata.
		On the positive side, we give an (optimal) PSPACE reachability algorithm for the case of initialized rectangular automata, where all analog variables follow trajectories within piecewise-linear envelopes and are reinitialized whenever the envelope changes.
	mtc.epfl.ch /~tah/Publications/whats_decidable_about_hybrid_automata.html (232 words)

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